Details

Time bar (total: 13.4s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms80×body80nan

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
26.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(sqrt (+ x 1.0))
54.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series323.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ 1.0 (sqrt (+ x 1.0)))
56.0ms
(sqrt (+ x 1.0))
217.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify883.0ms

Counts
80 → 80
Iterations

Useful iterations: done (880.0ms)

IterNodesCost
0146959
1343886
21581822
done5001816

prune190.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+ log1p-expm1-u
3×fma-def associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative hypot-def inv-pow
Counts
4 → 118
Calls
4 calls:
26.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(sqrt (+ x 1.0))
74.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
47.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
50.0ms
(sqrt (+ x 1.0))
172.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
113.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts
130 → 130
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01941642
14961444
225301264
done50001255

prune385.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
0.0b
(expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b
(* x (log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
17×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
10×add-exp-log
8×add-cbrt-cube
7×pow1
5×log1p-expm1-u
4×expm1-log1p-u associate-/r* distribute-lft-out add-log-exp
3×associate-*r* associate-*l* associate-/l*
2×div-exp associate-/r/
1×cbrt-undiv rec-exp log1p-udef expm1-log1p pow-flip frac-2neg flip3-+ 1-exp log1p-expm1 pow-prod-down prod-exp clear-num *-commutative cbrt-unprod flip-+ div-inv inv-pow expm1-udef unswap-sqr
Counts
4 → 81
Calls
4 calls:
0.0ms
(log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
0.0ms
(expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
7.0ms
(* x (log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))
46.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series2.4s

Counts
4 → 12
Calls
4 calls:
565.0ms
(log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
370.0ms
(expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
1.4s
(* x (log1p (expm1 (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))
133.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts
93 → 93
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01841521
14711347
225621204
done50011195

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))
0.0b
(fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
0.0b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
7.4b
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
248×times-frac
214×*-un-lft-identity
188×add-sqr-sqrt
160×unpow-prod-down
154×cube-prod
110×add-cube-cbrt
52×distribute-rgt-out
42×add-exp-log
36×sqr-pow
34×cube-mult unpow3
26×distribute-rgt1-in sqrt-prod distribute-lft-out
21×div-exp associate-/r*
20×associate-/l*
13×pow-to-exp pow-exp
11×add-cbrt-cube
9×prod-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv
2×cube-div frac-2neg clear-num associate-/r/ fma-udef div-inv unpow2
1×flip3-+ cbrt-unprod flip-+
Counts
4 → 359
Calls
4 calls:
39.0ms
(/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))
0.0ms
(fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
39.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))
1.0s
(fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
199.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
674.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3)) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

simplify694.0ms

Counts
371 → 371
Iterations

Useful iterations: done (675.0ms)

IterNodesCost
03568205
17696691
done50016410

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11512
done1512

end0.0ms

sample762.0ms

Algorithm
intervals
Results
404.0ms7997×body80valid
85.0ms2687×body80nan
0.0ms3×body1280valid